Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing

TL;DR

This work addresses the bottleneck of conventional OTAC, which computes a single function per transmission by using only the real signal component. It introduces Quadrature Over-the-Air Computing (Q-OTAC), which encodes two independent streams in the in-phase and quadrature components of a single complex transmission and recovers them with an IQ-decoupled MMSE combiner, effectively doubling the computation rate. The authors present a dual-stream transmitter design and a real-valued reformulation that yields closed-form MMSE combiners for each stream, enabling parallel computation of two nomographic functions (e.g., sums, products) at the AP. Simulations demonstrate reliable multimodal aggregation and about 5 dB NMSE improvement over single-stream OTAC, highlighting Q-OTAC’s potential for high-efficiency B5G/6G edge computing and multimodal sensing applications.

Abstract

We propose a novel quadrature over-the-air computing (Q-OTAC) framework that enables the simultaneously computation of two independent functions and/or data stream within a single transmission. In contrast to conventional OTAC schemes, where a single function is computed by treating each complex signal as a single component, the proposed Q-OTAC exploits both in-phase and quadrature (IQ) components of a complex signal, encoding two distinct functions and/or data streams at the edge devices (EDs) and employing a novel low-complexity IQ-decoupled combiner at the access point (AP) to independently recover each stream, which effectively doubles the computation rate. A key strength of this framework lies in its simplicity and broad compatibility: the extension into the quadrature domain is conceptually straightforward, yet remakably powerful, allowing seamless integration into existing OTAC techniques. Simulation results validate the effectiveness of this approach, including the first demonstration of dual-function aggregation (e.g., parallel summation and product), highlighting the potential of Q-OTAC for enabling multi-modal and high-efficiency beyond fifth generation (B5G) applications.

Figures (3)

• Figure 1: Illustration of the proposed Q-OTAC system.
• Figure 2: The NMSE CDF for different multimodal dual-stream Q-OTAC scenarios for $N = 20, K = 20$ and $\mathrm{SNR} = 15\mathrm{dB}$.
• Figure 3: Summation performance of the proposed Q-OTAC against the conventional OTAC, with $N = 20$, $K = 20$.